Solve centroid and mass distribution problems with flexible particle tables fast online. Handle 1D, 2D, 3D inputs, then download clear CSV or PDF summaries.
| Mass | x | y | z |
|---|---|---|---|
| 2 | 0 | 0 | 0 |
| 1 | 3 | 0 | 0 |
| 3 | 1 | 2 | 0 |
For discrete masses, the center of mass is the mass‑weighted average of positions. In 1D: x̄ = (Σ mᵢ xᵢ) / (Σ mᵢ).
In 2D and 3D the same idea applies component‑wise: ȳ = (Σ mᵢ yᵢ) / (Σ mᵢ), z̄ = (Σ mᵢ zᵢ) / (Σ mᵢ).
For composite objects, treat each part as a single mass located at its centroid. Sum all parts using the same equations above.
Center of mass (COM) condenses a distributed body into one effective point for translation. When forces act on a rigid object, predicting motion is simpler if you track COM and total mass. In lab work, COM helps validate sensor data, balance rigs, and compare prototypes consistently.
Many problems are naturally discrete: beads on a rod, satellites in a cluster, or masses on a frame. Composite analysis is equally common: split a body into parts with known centroids. Both cases use the same mass‑weighted average, so the calculator supports either workflow.
The COM coordinate is pulled toward larger masses. For example, masses 2 kg at x=0 m and 1 kg at x=3 m give x̄ = (2·0 + 1·3)/(2+1) = 1.000 m. A small added mass far away can still shift COM noticeably.
Use 1D for linear assemblies, 2D for planar layouts, and 3D for full spatial models. Results depend on your origin and axes, so define the coordinate frame carefully. A translated origin shifts COM coordinates by the same translation, which is expected.
Units do not change the physics, but they affect readability and reporting. Choose meters, centimeters, or inches to match measurement tools. Precision controls rounding only; it does not reduce experimental uncertainty. If mass values have ±1% error, COM can inherit similar relative uncertainty.
In structures, COM helps estimate tipping risk and support reactions. In robotics, COM influences gait stability and actuator sizing. In biomechanics, COM tracking approximates balance during motion capture. In aerospace, payload COM shifts affect trim and control margins during burns.
Continuous bodies use integrals: x̄ = (1/M)∫x dm. Practically, you approximate integrals by dividing a shape into many small elements, each with mass and centroid, then summing them like “composite parts.” Finer partitions usually improve accuracy.
Keep units consistent across all rows, and ensure masses are positive. Use negative coordinates when points lie left, below, or behind the origin. Verify that the number of rows used matches expectations, then export CSV or PDF for notebooks, reports, and peer review.
1) Can I compute COM for an object with holes?
Yes. Treat removed material as a negative “part” with the hole’s centroid and the removed mass. Keep the same coordinate frame for all parts, and the mass‑weighted sum will account for the void.
2) What happens if I enter mixed units in rows?
The calculator assumes every coordinate uses the same unit system. Mixed units will produce incorrect results because the weighted sums add incompatible lengths. Convert all coordinates to one unit before calculating.
3) Why is a row ignored in the calculation?
Rows are used only when mass is positive and required coordinates are provided for the chosen dimension. Empty fields, non‑numeric entries, or zero/negative masses are skipped to prevent misleading averages.
4) Does changing precision change the computed COM?
No. Precision only rounds what you see and what exports contain. Internally the calculation uses full floating‑point values from your inputs, then formats results to your selected decimals.
5) How do I model a long beam with varying density?
Divide the beam into segments where density is approximately constant. Compute each segment’s mass and centroid, enter them as composite parts, and calculate. More segments generally give a closer approximation to the continuous integral.
6) Can COM lie outside the physical object?
Yes. For shapes like a hollow ring, crescent, or L‑shaped bracket, the mass distribution can place COM in empty space. That is normal and still useful for predicting translational motion.
7) When should I use 2D versus 3D?
Use 2D when all points lie in a plane and out‑of‑plane variation is negligible. Use 3D when thickness, vertical offsets, or spatial placement matter, such as stacked components or volumetric assemblies.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.